Comment: I distinctly remember my Jr. High School Science teacher telling
my class (this was some time in the early 90s) that if a cat walked across
the Golden Gate Bridge (assuming nothing else was on it - no cars, etc.),
that the bridge would collapse. It had something to do with the rhythm of
the cat's paws and the construction of the bridge, i.e., the cables.
I remember coming home from school that day and telling my mother what I
learned. She looked at me like I had lost my mind. We moved to another
school shortly after that . . . But that was just a coincidence.
I'm assuming there's no validity to this claim??

I heard when I was a child that soldiers stopped marching when they crossed bridges in case the rhythm of their marching caused vibrations that made the bridge collapse. I have no ideas if soldiers stop marching on bridges, or if they did not if it would cause the bridge to collapse.

My understanding of the explanation is that the aeroelastic flutter is like the a violin bow exciting a string, and the string is going to vibrate at that frequency, because that's what strings do.

So the bridge oscillates at that frequency because that happens to be the frequency that it is going to oscillate at. The thing that destroyed it is that the oscillations kept building up and up rather than damping down.

A kind of feedback, like if you play certain notes on a guitar at just the right distance right in front of the speaker, it feeds back and just gets louder and louder and louder.

Last edited by Der Induktionator; 22 November 2008 at 05:32 PM.
Reason: forgot a couple words.

My understanding of the explanation is that the aeroelastic flutter is like the a violin bow exciting a string, and the string is going to vibrate at that frequency, because that's what strings do.

It's called the resonant frequency.

There's no way a cat could set up sufficient resonance in the Golden Gate Bridge even if it was walking at exactly the right frequency, though. The damping would be far too great, for one thing. (Meaning the vibrational energy would dissipate far too quickly to build up at all, let alone to a level that would destroy the bridge.)

And there's nothing special about a cat - I'd have thought a regular two-step like a person walking would be more likely to hit the resonant frequency than a four-footed gait. Neither would in the case of the Golden Gate, I'd imagine - presumably its main resonant frequencies are quite low. If a single cat could (in theory) do it, then so could a person. The idea's pretty much absurd, obviously.

The fundamental difference between a cat and the collapse of the 'Narrows is where the energy comes from.

It takes a certain amount of energy to destroy a bridge, and if the energy is coming from a cat, even a very skilled cat that is able to perfectly match a natural frequency of the bridge, a cat just doesn't have the energy.

The wind, on the other hand, even at low speeds, carries a tremendous amount of energy, and the 'narrows was unlucky enough to be very efficient at collecting that energy.

Marching soldiers and a small bouncy bridge? Well... there's a very bouncy bridge on a Wanderweg near here that gets uncomfortable to walk on if a couple people excite it.
I don't think we could collapse it because 1) it's steel and 2) it gets too uncomfortable to walk on to excite further, so we automatically break step to de-excite it.

My understanding of the explanation is that the aeroelastic flutter is like the a violin bow exciting a string, and the string is going to vibrate at that frequency, because that's what strings do.

So the bridge oscillates at that frequency because that happens to be the frequency that it is going to oscillate at. The thing that destroyed it is that the oscillations kept building up and up rather than damping down.

A kind of feedback, like if you play certain notes on a guitar at just the right distance right in front of the speaker, it feeds back and just gets louder and louder and louder.

Aeroelastic flutter though, is not the same as resonant frequency. The Wiki article actually does a good job of explaining the difference, and the fact that there is an ongoing myth that the Tacoma Narrows bridge failed due to resonant frequency

Aeroelastic flutter though, is not the same as resonant frequency. The Wiki article actually does a good job of explaining the difference, and the fact that there is an ongoing myth that the Tacoma Narrows bridge failed due to resonant frequency

erwins

Unfortunately most people still aren't going to understand the distinction, especially since at its collapse they see an oscillation. People are just going to see the oscillation and pick up on that, and certainly not look at the mechanism that continually coupled ever more and more energy into building it.

There's no way a cat could set up sufficient resonance in the Golden Gate Bridge even if it was walking at exactly the right frequency, though. The damping would be far too great, for one thing. (Meaning the vibrational energy would dissipate far too quickly to build up at all, let alone to a level that would destroy the bridge.) . . .

One of the more useful modeling tools in engineering is the "spring and dashpot" combination. Essentially, you take two masses -- for example, two planks of wood -- and couple them together with a spring -- and then, in parallel with the spring, you add a shock absorber. Think of the air-pressure piston that keeps the bathroom door from slamming shut in a restaurant. The spring and the resistant piston can have different physical values.

For instance, you might have a powerful spring and a weak piston: like a car where the shocks are blown out. You hit a bump, and you keep on a-rockin' for a long time down the road.

But the Golden Gate Bridge? That's a massively powerful spring and a gigantically powerful piston. The shock absorption effect is just titanic. You get heavily-laden big rigs rolling across it daily. A cat wouldn't even begin to register.

The theory in the OP might possibly be true if the bridge could be modeled by a spring alone, with no shock-absorbing capacity at all. An extremely taut wire, for instance, might be modeled that way. But in reality, the bridge has a vast amount of "stiffness" as well as its natural "springiness."

Way busted.

Silas

P.S. Richard W: this wasn't really directed at you, because I figure you already knew all this. Just using your post as a -- may I say it? -- springboard.

With some other non-English sources, I can add the following. The bridge went down in pretty low temperatures; there were no casualties. Initially the collapse has been attributed to the resonanse, but in the more recent studies the role of actually marching through the bridge is doubted. There are contradicting reports wheter the dragoons actually dismounted their horses or not, i.e. whether there was something to resonate in the first place.

The bridge has been called "singing". It is a chain bridge, and the chains produced a sound when people moved along the bridge. Since the breakdown occured in a pretty cold winter, it is a possibility that a combination of factors (perhaps, including the actual resonance) contributed to the failure; it is possible that resonance wasn't a part at all.

Anyways, after the fact all the thing has been blamed on resonance (perhaps, to avoid deeper probes). It became a textbook example and I think even made it into the military commands by creating a command that ordered not to go in sync specifically (I can't find anything on the latter part).

The thing people should keep in mind that a bit later, in mid-1940es there has been a lot of bridge crossings by a lot of soldiers. I'm not talking Golden Gate bridge, but much flimsier portable army bridges. For what I know, they were designed with resonance failure in mind, so it might be actually a good thing that this legend existed in the first place - of cource, if it is a legend.

That Mythbusters episode mentioned a pedestrian bridge that opened in London a few years back that was a little too densely packed its first day and that experienced a bit of the resonant frequency issue. It didn't cause any structural damage IIRC but it did freak out many of the people on the bridge so it was closed down and retrofitted.

A 20-second Google search revealed that this was the Millenium Bridge:

That Mythbusters episode mentioned a pedestrian bridge that opened in London a few years back that was a little too densely packed its first day and that experienced a bit of the resonant frequency issue. It didn't cause any structural damage IIRC but it did freak out many of the people on the bridge so it was closed down and retrofitted.

A 20-second Google search revealed that this was the Millenium Bridge:

I was going to mention that one earlier, but when I found a BBC archive article from the time, there was no mention specifically of resonance as being the problem, although I remembered it as being so.

Strangely, searching the BBC a second time seemed to bring up a different lot of articles. This page has a semi-technical discussion, and it sounds like a resonance problem to me, although from side to side making the bridge twist, rather than end to end, it seems.

Anyway, they added more dampers (again suggesting a resonance problem - at least, to a non-engineer like me) and reopened it shortly afterwards, and these days it only wobbles a bit. Although people still call it the "wobbly bridge".

Adam Hart-Davis did a programme on the Millennium Bridge (I think on his Science Shack series), and is was a resonance problem; but one thing they discovered that one person walking on the bridge would start it wobbling, and anyone else then going onto the bridge would then be forced to walk in rhythm due to the swaying of the bridge. The dampers fitted are effective in stopping this problem; essential as the bridge is one of the main accesses to the Tate Modern Gallery

Okay, it's pretty silly to say that a cat walking on a major bridge could build up enough energy to collapse the bridge. But ... could you fire a cat from a cannon or such with enough velocity to knock down a bridge?